Powering Arduino at 5VDC off 12VDC circuit

Hello all, nice place you have here.

I am sorry this question has probably been asked and answered many times here but I looked and couldn't seem to find a question that was close enough to mine so I decided just to ask.

I am using a nickel-chomium resistance heater and I want to control it like a thermostat. I can handle all that, my question is about power source(s). I want to use a single 12VDC power supply to run both the heater and the Arduino. The heater has 4 ohms so that is about 3 amps. I will use a power MOSFET to turn the heater on and off with the gate controlled by my Arduino running at 5VD.

Would it be a bad idea to simply put a 5VDC voltage regulator on the incoming 12VDC rail and power the Arduino off of that? Most of the current should be headed to the heater but I am worried that a passive voltage regulator might be under spec and I may as well just spend the money on a DC to DC converter.

Thank you and sorry again if this has been answered already.

Your arduino draws very little current, tens of mA.
Try it with the 12V feeding the onboard barrel jack.
If you see upsets when the MOSFET switches, then look into the external regulator.
This would be good and not much money.